Greenwood press

82
PROPORTIONS
The shadow produced on the ground at
noon at Alexandria based on an angle
of elevation of 
α degrees.

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Therefore the distance from Cyrene to Alexandria represented 7.2/360 of the
earth’s circumference, since there are 360 degrees in a circle. Using the proportion,
7.2 degrees between cities
360 degrees in circle
=
5000 stades between cities
number of stades around earth
,
Eratosthenes determined that the distance around the earth is about 250,000
stades, or 139,750,000 feet. Since the cross section of the earth is approximately
a circle, the radius can be determined by using the equation 
c = 2πr, comparing
the circumference, 
c, to its radius, r. Substituting the value c = 139,750,000 feet
and solving the equation will show that the radius of the earth is about 22,241,900
feet, or 4,214 miles. That’s only 6 percent off the actual distance of 3,963 miles!
Movie screens are created to handle film with specific dimensions. Suppose
the width of each film cell is 5.48 cm and the height is 2.30 cm. An ideal movie
screen would show the entire picture without cropping out any of the sides. A
small movie theater may leave a horizontal length of 7 meters, about 23 feet, to
place its screen. In order to project the film perfectly on the screen, a proportion
comparing the height and width needs to be used so that the correct height of the
screen can be accurately determined. The height of the screen, 
h, is equal to ap-
proximately 2.94 meters, or 9.66 feet, by solving the equation determined by the
proportion
h vertical meters on screen
2.30 vertical cm on film
=
7 horizontal meters on screen
5.48 vertical cm on film
.
Proportions are used to predict the mass of a dinosaur with scaled models.
Since a model is a miniature version of the actual dinosaur, paleontologists use
the ratio
length of actual dinosaur
3
length of model
3
=
volume of actual dinosaur
volume of model
.
This ratio is cubed, because volume is a three-dimensional concept, compared to
a one-dimensional concept of length. For example, the volume of a cube is the